Deck 12: Multiple Regression and Model Building

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سؤال
It is safe to conduct t-tests on the individual β parameters in a first-order linear model in order to determine which independent variables are useful for predicting y and which are not.
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لقلب البطاقة.
سؤال
A qualitative variable whose outcomes are assigned numerical values is called a coded variable.
سؤال
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary  <div style=padding-top: 35px>
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سؤال
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary <strong>A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary   Interpret the coefficient for the tuition variable shown on the printout.</strong> A) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will decrease by $203,402, holding the GMAT score constant. B) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will increase by $394.12, holding the GMAT score constant C) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will increase by $920.12, holding the GMAT score constant D) For every $1000 increase in the average starting salary, we estimate that the tuition charged by the MBA program will increase by $920.12. <div style=padding-top: 35px> Interpret the coefficient for the tuition variable shown on the printout.

A) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will decrease by $203,402, holding the GMAT score constant.
B) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will increase by $394.12, holding the GMAT score constant
C) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will increase by $920.12, holding the GMAT score constant
D) For every $1000 increase in the average starting salary, we estimate that the tuition charged by the MBA program will increase by $920.12.
سؤال
Why is the random error term ε added to a multiple regression model? 12.2 Estimating and Making Inferences about the β Parameters 1 Write First-Order Model
سؤال
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):  <div style=padding-top: 35px>
سؤال
For a multiple regression model, we assume that the mean of the probability distribution of the random error is 0.
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In the first-order model E(y)=β0+β1x1+β2x2+β3x3,β2E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } , \beta _ { 2 } represents the slope of the line relating yy to x2x _ { 2 } when β1\beta _ { 1 } and β3\beta _ { 3 } are both held fixed.
سؤال
Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive:  <div style=padding-top: 35px>
سؤال
Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive:  <div style=padding-top: 35px>
سؤال
A first-order model does not contain any higher-order terms.
سؤال
A first-order model may include terms for both quantitative and qualitative independent variables.
سؤال
The method of fitting first-order models is the same as that of fitting the simple straight-line model, i.e. the method of least squares.
سؤال
The printout shows the results of a first-order regression analysis relating the sales price y of a product to the time in hours x1 and the cost of raw materials x2 needed to make the product. The printout shows the results of a first-order regression analysis relating the sales price y of a product to the time in hours x1 and the cost of raw materials x2 needed to make the product.   a. What is the least squares prediction equation? b. Identify the SSE from the printout. c. Find the estimator of σ2 for the model.<div style=padding-top: 35px> a. What is the least squares prediction equation? b. Identify the SSE from the printout. c. Find the estimator of σ2 for the model.
سؤال
A term that contains the value of a quantitative variable raised to the second power is called a higher -order term.
سؤال
Probabilistic models that include more than one dependent variable are called multiple regression models.
سؤال
A statistics professor gave three quizzes leading up to the first test in his class. The quiz grades and test grade for each of eight students are given in the table. A statistics professor gave three quizzes leading up to the first test in his class. The quiz grades and test grade for each of eight students are given in the table.   The professor would like to use the data to find a first-order model that he might use to predict a student's grade on the first test using that student's grades on the first three quizzes. a. Identify the dependent and independent variables for the model. b. What is the least squares prediction equation? c. Find the SSE and the estimator of σ2 for the model. 2 Find and Interpret Sample Estimates for β Parameters<div style=padding-top: 35px> The professor would like to use the data to find a first-order model that he might use to predict a student's grade on the first test using that student's grades on the first three quizzes. a. Identify the dependent and independent variables for the model. b. What is the least squares prediction equation? c. Find the SSE and the estimator of σ2 for the model. 2 Find and Interpret Sample Estimates for β Parameters
سؤال
The value of R2 is only useful when the number of data points is substantially larger than the number of β parameters in the model.
سؤال
Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive:   2 Find and Interpret Confidence Interval<div style=padding-top: 35px> 2 Find and Interpret Confidence Interval
سؤال
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary  <div style=padding-top: 35px>
سؤال
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary <strong>A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary   Interpret the coefficient of determination value shown in the printout.</strong> A) We can explain 68.57% of the variation in the average starting salaries around their mean using the model that includes the average GMAT score and the tuition for the MBA program. B) We expect most of the average starting salaries to fall within $41,353 of their least squares predicted values. C) We expect most of the average starting salaries to fall within $20,676 of their least squares predicted values. D) At α = 0.05, there is insufficient evidence to indicate that something in the regression model is useful for predicting the average starting salary of the graduates of an MBA program. <div style=padding-top: 35px> Interpret the coefficient of determination value shown in the printout.

A) We can explain 68.57% of the variation in the average starting salaries around their mean using the model that includes the average GMAT score and the tuition for the MBA program.
B) We expect most of the average starting salaries to fall within $41,353 of their least squares predicted values.
C) We expect most of the average starting salaries to fall within $20,676 of their least squares predicted values.
D) At α = 0.05, there is insufficient evidence to indicate that something in the regression model is useful for predicting the average starting salary of the graduates of an MBA program.
سؤال
A statistics professor gave three quizzes leading up to the first test in his class. The quiz grades and test grade for each of eight students are given in the table. A statistics professor gave three quizzes leading up to the first test in his class. The quiz grades and test grade for each of eight students are given in the table.   The professor fit a first-order model to the data that he intends to use to predict a student's grade on the first test using that student's grades on the first three quizzes.   α = .05. Interpret the result. 12.4 Using the Model for Estimation and Prediction 1 Find and Interpret Prediction Interval<div style=padding-top: 35px> The professor fit a first-order model to the data that he intends to use to predict a student's grade on the first test using that student's grades on the first three quizzes. A statistics professor gave three quizzes leading up to the first test in his class. The quiz grades and test grade for each of eight students are given in the table.   The professor fit a first-order model to the data that he intends to use to predict a student's grade on the first test using that student's grades on the first three quizzes.   α = .05. Interpret the result. 12.4 Using the Model for Estimation and Prediction 1 Find and Interpret Prediction Interval<div style=padding-top: 35px> α = .05. Interpret the result. 12.4 Using the Model for Estimation and Prediction 1 Find and Interpret Prediction Interval
سؤال
In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x1) and the number of checks cashed per day (x2). Data collected for n = 20 working days were used to fit the model: E(y)=β0+β1x1+β2x2E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }

A partial printout for the analysis follows:

 ActualPredict  Lower 95% CL Upper 95% CL  OBS  X1  X2  Value  Value  Residual  Predict  Predict 1778164474.70783.1758.46847.224119.126\begin{array}{rrrrrrrr}\hline&&&\text { Actual}&\text {Predict } &&\text { Lower 95\% CL}&\text { Upper 95\% CL }\\\text { OBS } & \text { X1 } & \text { X2 } & \text { Value } & \text { Value } & \text { Residual } & \text { Predict } & \text { Predict } \\1 & 7781 & 644 & 74.707 & 83.175 & -8.468 & 47.224 & 119.126\\\hline \end{array} Interpret the 95% prediction interval for y shown on the printout.

A) We are 95% confident that between 47.224 and 119.126 man-hours will be worked during a single day in which 7,781 pieces of mail are processed and 644 checks are cashed.
B) We expect to predict number of man-hours worked per day to within an amount between 47.224 and 119.126 of the true value.
C) We are 95% confident that the number of man-hours worked per day falls between 47.224 and 119.126.
D) We are 95% confident that the mean number of man-hours worked per day falls between 47.224 and 119.126 for all days in which 7,781 pieces of mail are processed and 644 checks are cashed.
سؤال
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):  <div style=padding-top: 35px>
سؤال
The confidence interval for the mean E(y) is narrower that the prediction interval for y.
سؤال
The table below shows data for n = 20 observations. The table below shows data for n = 20 observations.    <div style=padding-top: 35px> The table below shows data for n = 20 observations.    <div style=padding-top: 35px>
سؤال
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):  <div style=padding-top: 35px>
سؤال
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary <strong>A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary   The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the tuition charged by the MBA program was $75,000 and the GMAT score was 675. The results are shown here: 95% confidence interval for E(Y): ($126,610, $136,640) 95% prediction interval for Y: ($90,113, $173,160) Which of the following interpretations is correct if you want to use the model to estimate Y for a single MBA program?</strong> A) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $126,610 and $136,640. B) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $90,113 and $173,16,30. C) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $126,610 and $136,640. D) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $90,113 and $173,16,30. <div style=padding-top: 35px> The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the tuition charged by the MBA program was $75,000 and the GMAT score was 675. The results are shown here: 95% confidence interval for E(Y): ($126,610, $136,640) 95% prediction interval for Y: ($90,113, $173,160) Which of the following interpretations is correct if you want to use the model to estimate Y for a single MBA program?

A) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $126,610 and $136,640.
B) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $90,113 and $173,16,30.
C) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $126,610 and $136,640.
D) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $90,113 and
$173,16,30.
سؤال
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):  <div style=padding-top: 35px>
سؤال
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):  <div style=padding-top: 35px>
سؤال
In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x1) and the number of checks cashed per day (x2). Data collected for n = 20 working days were used to fit the model: In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x1) and the number of checks cashed per day (x2). Data collected for n = 20 working days were used to fit the model:  <div style=padding-top: 35px>
سؤال
Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive:  <div style=padding-top: 35px>
سؤال
In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x1) and the number of checks cashed per day (x2). Data collected for n = 20 working days were used to fit the model: In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x1) and the number of checks cashed per day (x2). Data collected for n = 20 working days were used to fit the model:  <div style=padding-top: 35px>
سؤال
During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first three tests. To test this claim, multiple regression will be used to model Test 4 score (y), as a function of Test1 score (x1)\left( x _ { 1 } \right) , Test 2 score (x2)\left( x _ { 2 } \right) , and Test3 score (x3)\left( x _ { 3 } \right) . [Note: All test scores range from 200 to 800 , with higher scores indicative of a higher quality product.] Consider the model:
E(y)=β1+β1x1+β2x2+β3x3E ( y ) = \beta _ { 1 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 }
The global FF statistic is used to test the null hypothesis, H0:β1=β2=β3=0H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0 . Describe this hypothesis in words.

A) The model is not statistically useful for predicting Test4 score.
B) The model is statistically useful for predicting Test4 score.
C) The first three test scores are poor predictors of Test4 score.
D) The first three test scores are reliable predictors of Test4 score.
سؤال
During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first three tests. To test this claim, multiple regression will be used to model Test4 score (y), as a function of Test1 score (x1), Test 2 score (x2), and Test3 score (x3). [Note: All test scores range from 200 to 800, with higher scores indicative of a higher quality product.] Consider the model: E(y)=β1+β1x1+β2x2+β3x3E ( y ) = \beta _ { 1 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } The first-order model was fit to the data for each of 12 units sampled from the production line. A 95% prediction interval for Test4 score of a product with Test1 = 590, Test2 = 750, and Test3 = 710 is (583, 793). Interpret this result.

A) We are 95% confident that a product's Test4 score will fall between 583 and 793 points when the first three scores are 590, 750, and 710, respectively.
B) We are 95% confident that a product's Test4 score increases by an amount between 583 and 793 points for every 1 point increase in Test1 score, holding Test 2 and Test 3 score constant.
C) Since 0 is outside the interval, there is evidence of a linear relationship between Test4 score and any of the other test scores.
D) We are 95% confident that the mean Test4 score of all manufactured products falls between 583 and 793 points.
سؤال
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):  <div style=padding-top: 35px>
سؤال
The rejection of the null hypothesis in a global F-test means that the model is the best model for providing reliable estimates and predictions.
سؤال
The complete second-order model with two quantitative independent variables does not allow for interaction between the two independent variables.
سؤال
A college admissions officer proposes to use regression to model a student's college GPA at graduation in terms of the following two variables: A college admissions officer proposes to use regression to model a student's college GPA at graduation in terms of the following two variables:   Explain how to determine if the relationship between college GPA and SAT score depends on the high school GPA.<div style=padding-top: 35px> Explain how to determine if the relationship between college GPA and SAT score depends on the high school GPA.
سؤال
The concessions manager at a beachside park recorded the high temperature, the number of people at the park, and the number of bottles of water sold for each of 12 consecutive Saturdays. The data are shown below. The concessions manager at a beachside park recorded the high temperature, the number of people at the park, and the number of bottles of water sold for each of 12 consecutive Saturdays. The data are shown below.     12.5 Interaction Models 1 Write Interaction Model<div style=padding-top: 35px> The concessions manager at a beachside park recorded the high temperature, the number of people at the park, and the number of bottles of water sold for each of 12 consecutive Saturdays. The data are shown below.     12.5 Interaction Models 1 Write Interaction Model<div style=padding-top: 35px> 12.5 Interaction Models 1 Write Interaction Model
سؤال
In the quadratic model E(y)=β0+β1x+β2x2, a negative value of β1E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } , \text { a negative value of } \beta _ { 1 } indicates downward concavity.
سؤال
Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: y=y = Retail PRICE (measured in dollars)
x1=x _ { 1 } = Microprocessor SPEED (measured in megahertz)
(Values in sample range from 10 to 40 )
x2=x _ { 2 } = CHIP size (measured in computer processing units)
(Values in sample range from 286 to 486 )
a first-order regression model was fit to the data. Part of the printout follows:
 Dep Var Predict Std Err Lower 95% Upper 95% OBS SPEED CHIP PRICE Value Predict Predict Predict Residual1332865099.04464.9260.7683942.74987.1634.1\begin{array}{lllllllll}\hline &&&\text { Dep Var }&\text {Predict }&\text {Std Err}&\text { Lower 95\%}&\text { Upper 95\% }\\ \text {OBS }&\text {SPEED }&\text {CHIP }&\text {PRICE}&\text { Value }&\text {Predict }&\text {Predict}&\text { Predict }&\text {Residual}\\1 & 33 & 286 & 5099.0 & 4464.9 & 260.768 & 3942.7 & 4987.1 & 634.1\\\hline \end{array}
Interpret the interval given in the printout.

A) We are 95% confident that the price of a single hard drive with 33 megahertz speed and 386 CPU falls between $3,943 and $4,987.
B) We are 95% confident that the price of a single hard drive falls between $3,943 and $4,987.
C) We are 95% confident that the average price of all hard drives falls between $3,943 and $4,987.
D) We are 95% confident that the average price of all hard drives with 33 megahertz speed and 386 CPU falls between $3,943 and $4,987.
سؤال
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary <strong>A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary   The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the tuition charged by the MBA program was $75,000 and the GMAT score was 675. The results are shown here: 95% confidence interval for E(Y): ($126,610, $136,640) 95% prediction interval for Y: ($90,113, $173,160) Which of the following interpretations is correct if you want to use the model to estimate E(Y) for all MBA programs?</strong> A) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $126,610 and $136,640. B) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $90,113 and $173,16,30. C) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $126,610 and $136,640. D) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $90,113 and $173,16,30. <div style=padding-top: 35px> The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the tuition charged by the MBA program was $75,000 and the GMAT score was 675. The results are shown here: 95% confidence interval for E(Y): ($126,610, $136,640) 95% prediction interval for Y: ($90,113, $173,160) Which of the following interpretations is correct if you want to use the model to estimate E(Y) for all MBA programs?

A) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $126,610 and $136,640.
B) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $90,113 and $173,16,30.
C) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $126,610 and $136,640.
D) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $90,113 and
$173,16,30.
سؤال
One of three surfaces is produced by a complete second-order model with two quantitative independent variables: a paraboloid that opens upward, a paraboloid that opens downward, or a saddle -shaped surface.
سؤال
Once interaction has been established between x1x _ { 1 } and x2x _ { 2 } , the first-order terms for x1x _ { 1 } and x2x _ { 2 } may be deleted from the regression model leaving the higher-order term containing the product of x1x _ { 1 } and x2x _ { 2 } .
سؤال
In an interaction model, the relationship between E(y)E ( y ) and x1x _ { 1 } is linear for each fixed value of x2x _ { 2 } but the slopes of the lines relating E(y)E ( y ) and x1x _ { 1 } may be different for two different fixed values of x2x _ { 2 } .
سؤال
 <div style=padding-top: 35px>
سؤال
A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model  <div style=padding-top: 35px>
سؤال
A college admissions officer proposes to use regression to model a student's college GPA at graduation in terms of the following two variables: A college admissions officer proposes to use regression to model a student's college GPA at graduation in terms of the following two variables:   The admissions officer believes the relationship between college GPA and high school GPA is linear and the relationship between SAT score and college GPA is linear. She also believes that the relationship between college GPA and high school GPA depends on the student's SAT score. Write the regression model she should fit. 2 Test if Model is Useful for Predicting y<div style=padding-top: 35px> The admissions officer believes the relationship between college GPA and high school GPA is linear and the relationship between SAT score and college GPA is linear. She also believes that the relationship between college GPA and high school GPA depends on the student's SAT score. Write the regression model she should fit. 2 Test if Model is Useful for Predicting y
سؤال
Which equation represents a complete second-order model for two quantitative independent variables? Which equation represents a complete second-order model for two quantitative independent variables?  <div style=padding-top: 35px>
سؤال
Consider the interaction model E(y)=7+3x14x2+5x1x2E ( y ) = 7 + 3 x _ { 1 } - 4 x _ { 2 } + 5 x _ { 1 } x _ { 2 } . Find the slope of the line relating E(y)E ( y ) and x1x _ { 1 } when x2=2x _ { 2 } = 2 when x2 = 2.

A) 13
B) 10
C) 1
D) 16
سؤال
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary  <div style=padding-top: 35px>
سؤال
Consider the partial printout below. Consider the partial printout below.   Is there evidence (at α = .05) that x1 and x2 interact? Explain. 12.6 Quadratic and Other Higher Order Models 1 Write and Interpret Second-Order Model<div style=padding-top: 35px> Is there evidence (at α = .05) that x1 and x2 interact? Explain. 12.6 Quadratic and Other Higher Order Models 1 Write and Interpret Second-Order Model
سؤال
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary  <div style=padding-top: 35px>
سؤال
We decide to conduct a multiple regression analysis to predict the attendance at a major league baseball game. We use the size of the stadium as a quantitative independent variable and the type of game as a qualitative variable (with two levels - day game or night game). We hypothesize the following model: E(y)=β0+β1x1+β2x2+β3x3E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 }
Where x1=\mathrm { x } _ { 1 } = size of the stadium
x2=1\mathrm { x } _ { 2 } = 1 if a day game, 0 if a night game

A plot of the yx1y - x _ { 1 } relationship would show: :

A) Two parallel curves
B) Two non-parallel curves
C) Two non-parallel lines
D) Two parallel lines
سؤال
Consider the partial printout for an interaction regression analysis of the relationship between a dependent variable y and two independent variables x1 and x2. Consider the partial printout for an interaction regression analysis of the relationship between a dependent variable y and two independent variables x1 and x2.     3 Test for Interaction Between Two Variables<div style=padding-top: 35px> Consider the partial printout for an interaction regression analysis of the relationship between a dependent variable y and two independent variables x1 and x2.     3 Test for Interaction Between Two Variables<div style=padding-top: 35px> 3 Test for Interaction Between Two Variables
سؤال
 The independent variables x1 and x2 interact when the effect on E(y) of a change in x1 depends on x2\text { The independent variables } x _ { 1 } \text { and } x _ { 2 } \text { interact when the effect on } E ( y ) \text { of a change in } x _ { 1 } \text { depends on } x _ { 2 } \text {. }
سؤال
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model  <div style=padding-top: 35px>
سؤال
When testing the utility of the quadratic model E(y)=β0+β1x+β2x2E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } , the most important tests involve the null hypotheses H0:β0=0H _ { 0 } : \beta 0 = 0 and H0:β1=0H _ { 0 } : \beta _ { 1 } = 0 .
سؤال
A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model E(y)=β0+β1x+β2x2E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }
This model was fit to data collected for a sample of 32 clocks sold at auction; a portion of the printout follows:
 PARAMETER STANDARD  T FOR 0:  VARIABLES  ESTIMATE  ERROR  PARAMETER =0 PROB >T INTERCEPT 286.429.6629.64.0001X.31.065.14.0016XX.000067.00007.95.3600\begin{array}{lrrrr}\hline &\text { PARAMETER }& \text {STANDARD }& \text { T FOR 0: }\\\text { VARIABLES } & \text { ESTIMATE } & \text { ERROR } & \text { PARAMETER }=0 & \text { PROB }>|T|\\\text { INTERCEPT } & 286.42 & 9.66 & 29.64 & .0001 \\\mathrm{X} & -.31 & .06 & -5.14 & .0016 \\\mathrm{X} \cdot \mathrm{X} & .000067 & .00007 & .95 & .3600 \\\hline\end{array}

Give the pp -value for testing H0:β2=0H _ { 0 } : \beta _ { 2 } = 0 against Ha:β20H _ { a } : \beta 2 \neq 0 .

A) .36
B) .0016
C) .18
D) .05
سؤال
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model  <div style=padding-top: 35px>
سؤال
When using the model E(y) = β0 + β1x for one qualitative independent variable with a 0-1 coding convention, β1 represents the difference between the mean responses for the level assigned the value 1 and the base level.
سؤال
The complete second-order model The complete second-order model   data points. The printout is shown below.     3 Test if Model is Useful for Predicting y<div style=padding-top: 35px> data points. The printout is shown below. The complete second-order model   data points. The printout is shown below.     3 Test if Model is Useful for Predicting y<div style=padding-top: 35px> The complete second-order model   data points. The printout is shown below.     3 Test if Model is Useful for Predicting y<div style=padding-top: 35px> 3 Test if Model is Useful for Predicting y
سؤال
A study of the top MBA programs attempted to predict y = the average starting salary (in $1000's) of graduates of the program based on x = the amount of tuition (in $1000's) charged by the program. After first considering a simple linear model, it was decided that a quadratic model should be proposed. Which of the following models proposes a 2nd-order quadratic relationship between x and y? A study of the top MBA programs attempted to predict y = the average starting salary (in $1000's) of graduates of the program based on x = the amount of tuition (in $1000's) charged by the program. After first considering a simple linear model, it was decided that a quadratic model should be proposed. Which of the following models proposes a 2nd-order quadratic relationship between x and y?  <div style=padding-top: 35px>
سؤال
What relationship between x and y is suggested by the scattergram? <strong>What relationship between x and y is suggested by the scattergram?  </strong> A) a quadratic relationship with downward concavity B) a quadratic relationship with upward concavity C) a linear relationship with positive slope D) a linear relationship with negative slope <div style=padding-top: 35px>

A) a quadratic relationship with downward concavity
B) a quadratic relationship with upward concavity
C) a linear relationship with positive slope
D) a linear relationship with negative slope
سؤال
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary  <div style=padding-top: 35px>
سؤال
When modeling E(y) with a single qualitative independent variable, the number of 0-1 dummy variables in the model is equal to the number of levels of the qualitative variable.
سؤال
Consider the second-order model Consider the second-order model  <div style=padding-top: 35px>
سؤال
The table shows the profit y (in thousands of dollars) that a company made during a month when the price of its product was x dollars per unit. The table shows the profit y (in thousands of dollars) that a company made during a month when the price of its product was x dollars per unit.   4 Perform Quadratic Regression and Make Predictions<div style=padding-top: 35px> 4 Perform Quadratic Regression and Make Predictions
سؤال
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary  <div style=padding-top: 35px>
سؤال
A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model E(y)=β0+β1x+β2x2E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }
This model was fit to data collected for a sample of 32 clocks sold at auction; a portion of the printout follows:
 PARAMETER STANDARD  T FOR 0:  VARIABLES  ESTIMATE  ERROR  PARAMETER =0 PROB >T INTERCEPT 286.429.6629.64.0001X.31.065.14.0016XX.000067.00007.95.3600\begin{array}{lrrrr}\hline &\text { PARAMETER }& \text {STANDARD }& \text { T FOR 0: }\\\text { VARIABLES } & \text { ESTIMATE } & \text { ERROR } & \text { PARAMETER }=0 & \text { PROB }>|T|\\\text { INTERCEPT } & 286.42 & 9.66 & 29.64 & .0001 \\\mathrm{X} & -.31 & .06 & -5.14 & .0016 \\\mathrm{X} \cdot \mathrm{X} & .000067 & .00007 & .95 & .3600 \\\hline\end{array}

Find the pp -value for testing H0:β2=0H _ { 0 } : \beta _ { 2 } = 0 against Ha:β2>0H _ { \mathbf { a } } : \beta _ { 2 } > 0 .

A) .18
B) .36
C) .0016
D) .05
سؤال
A graphing calculator was used to fit the model E(y) = ?0 + ?1x + ?2x2 to a set of data. The resulting screen is shown below.  <strong>A graphing calculator was used to fit the model E(y) = ?0 + ?1x + ?2x2 to a set of data. The resulting screen is shown below.   Which number on the screen represents the estimator of  \beta _ { 2 }  ?</strong> A) .9286 B) 5.5 C) 11 D) .9405 <div style=padding-top: 35px>  Which number on the screen represents the estimator of β2\beta _ { 2 } ?

A) .9286
B) 5.5
C) 11
D) .9405
سؤال
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model  <div style=padding-top: 35px>
سؤال
Consider the data given in the table below. Consider the data given in the table below.   a. Plot the data on a scattergram. Does a quadratic model seem to be a good fit for the data? Explain. b. Use the method of least squares to find a quadratic prediction equation. c. Graph the prediction equation on your scattergram. 12.7 Qualitative (Dummy) Variable Models 1 Write and Interpret Model with Qualitative Variables<div style=padding-top: 35px> a. Plot the data on a scattergram. Does a quadratic model seem to be a good fit for the data? Explain. b. Use the method of least squares to find a quadratic prediction equation. c. Graph the prediction equation on your scattergram. 12.7 Qualitative (Dummy) Variable Models 1 Write and Interpret Model with Qualitative Variables
سؤال
Consider the data given in the table below. Consider the data given in the table below.   Plot the data on a scattergram. Does a second-order model seem to be a good fit for the data? Explain.<div style=padding-top: 35px> Plot the data on a scattergram. Does a second-order model seem to be a good fit for the data? Explain.
سؤال
A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model  <div style=padding-top: 35px>
سؤال
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model  <div style=padding-top: 35px>
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Deck 12: Multiple Regression and Model Building
1
It is safe to conduct t-tests on the individual β parameters in a first-order linear model in order to determine which independent variables are useful for predicting y and which are not.
False
2
A qualitative variable whose outcomes are assigned numerical values is called a coded variable.
True
3
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary
C
4
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5
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary <strong>A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary   Interpret the coefficient for the tuition variable shown on the printout.</strong> A) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will decrease by $203,402, holding the GMAT score constant. B) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will increase by $394.12, holding the GMAT score constant C) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will increase by $920.12, holding the GMAT score constant D) For every $1000 increase in the average starting salary, we estimate that the tuition charged by the MBA program will increase by $920.12. Interpret the coefficient for the tuition variable shown on the printout.

A) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will decrease by $203,402, holding the GMAT score constant.
B) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will increase by $394.12, holding the GMAT score constant
C) For every $1000 increase in the tuition charged by the MBA program, we estimate that the average starting salary will increase by $920.12, holding the GMAT score constant
D) For every $1000 increase in the average starting salary, we estimate that the tuition charged by the MBA program will increase by $920.12.
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6
Why is the random error term ε added to a multiple regression model? 12.2 Estimating and Making Inferences about the β Parameters 1 Write First-Order Model
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7
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):
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8
For a multiple regression model, we assume that the mean of the probability distribution of the random error is 0.
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9
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10
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11
In the first-order model E(y)=β0+β1x1+β2x2+β3x3,β2E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } , \beta _ { 2 } represents the slope of the line relating yy to x2x _ { 2 } when β1\beta _ { 1 } and β3\beta _ { 3 } are both held fixed.
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12
Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive:
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13
Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive:
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14
A first-order model does not contain any higher-order terms.
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15
A first-order model may include terms for both quantitative and qualitative independent variables.
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16
The method of fitting first-order models is the same as that of fitting the simple straight-line model, i.e. the method of least squares.
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17
The printout shows the results of a first-order regression analysis relating the sales price y of a product to the time in hours x1 and the cost of raw materials x2 needed to make the product. The printout shows the results of a first-order regression analysis relating the sales price y of a product to the time in hours x1 and the cost of raw materials x2 needed to make the product.   a. What is the least squares prediction equation? b. Identify the SSE from the printout. c. Find the estimator of σ2 for the model. a. What is the least squares prediction equation? b. Identify the SSE from the printout. c. Find the estimator of σ2 for the model.
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18
A term that contains the value of a quantitative variable raised to the second power is called a higher -order term.
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19
Probabilistic models that include more than one dependent variable are called multiple regression models.
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20
A statistics professor gave three quizzes leading up to the first test in his class. The quiz grades and test grade for each of eight students are given in the table. A statistics professor gave three quizzes leading up to the first test in his class. The quiz grades and test grade for each of eight students are given in the table.   The professor would like to use the data to find a first-order model that he might use to predict a student's grade on the first test using that student's grades on the first three quizzes. a. Identify the dependent and independent variables for the model. b. What is the least squares prediction equation? c. Find the SSE and the estimator of σ2 for the model. 2 Find and Interpret Sample Estimates for β Parameters The professor would like to use the data to find a first-order model that he might use to predict a student's grade on the first test using that student's grades on the first three quizzes. a. Identify the dependent and independent variables for the model. b. What is the least squares prediction equation? c. Find the SSE and the estimator of σ2 for the model. 2 Find and Interpret Sample Estimates for β Parameters
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21
The value of R2 is only useful when the number of data points is substantially larger than the number of β parameters in the model.
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22
Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive:   2 Find and Interpret Confidence Interval 2 Find and Interpret Confidence Interval
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23
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary
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24
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary <strong>A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary   Interpret the coefficient of determination value shown in the printout.</strong> A) We can explain 68.57% of the variation in the average starting salaries around their mean using the model that includes the average GMAT score and the tuition for the MBA program. B) We expect most of the average starting salaries to fall within $41,353 of their least squares predicted values. C) We expect most of the average starting salaries to fall within $20,676 of their least squares predicted values. D) At α = 0.05, there is insufficient evidence to indicate that something in the regression model is useful for predicting the average starting salary of the graduates of an MBA program. Interpret the coefficient of determination value shown in the printout.

A) We can explain 68.57% of the variation in the average starting salaries around their mean using the model that includes the average GMAT score and the tuition for the MBA program.
B) We expect most of the average starting salaries to fall within $41,353 of their least squares predicted values.
C) We expect most of the average starting salaries to fall within $20,676 of their least squares predicted values.
D) At α = 0.05, there is insufficient evidence to indicate that something in the regression model is useful for predicting the average starting salary of the graduates of an MBA program.
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25
A statistics professor gave three quizzes leading up to the first test in his class. The quiz grades and test grade for each of eight students are given in the table. A statistics professor gave three quizzes leading up to the first test in his class. The quiz grades and test grade for each of eight students are given in the table.   The professor fit a first-order model to the data that he intends to use to predict a student's grade on the first test using that student's grades on the first three quizzes.   α = .05. Interpret the result. 12.4 Using the Model for Estimation and Prediction 1 Find and Interpret Prediction Interval The professor fit a first-order model to the data that he intends to use to predict a student's grade on the first test using that student's grades on the first three quizzes. A statistics professor gave three quizzes leading up to the first test in his class. The quiz grades and test grade for each of eight students are given in the table.   The professor fit a first-order model to the data that he intends to use to predict a student's grade on the first test using that student's grades on the first three quizzes.   α = .05. Interpret the result. 12.4 Using the Model for Estimation and Prediction 1 Find and Interpret Prediction Interval α = .05. Interpret the result. 12.4 Using the Model for Estimation and Prediction 1 Find and Interpret Prediction Interval
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26
In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x1) and the number of checks cashed per day (x2). Data collected for n = 20 working days were used to fit the model: E(y)=β0+β1x1+β2x2E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }

A partial printout for the analysis follows:

 ActualPredict  Lower 95% CL Upper 95% CL  OBS  X1  X2  Value  Value  Residual  Predict  Predict 1778164474.70783.1758.46847.224119.126\begin{array}{rrrrrrrr}\hline&&&\text { Actual}&\text {Predict } &&\text { Lower 95\% CL}&\text { Upper 95\% CL }\\\text { OBS } & \text { X1 } & \text { X2 } & \text { Value } & \text { Value } & \text { Residual } & \text { Predict } & \text { Predict } \\1 & 7781 & 644 & 74.707 & 83.175 & -8.468 & 47.224 & 119.126\\\hline \end{array} Interpret the 95% prediction interval for y shown on the printout.

A) We are 95% confident that between 47.224 and 119.126 man-hours will be worked during a single day in which 7,781 pieces of mail are processed and 644 checks are cashed.
B) We expect to predict number of man-hours worked per day to within an amount between 47.224 and 119.126 of the true value.
C) We are 95% confident that the number of man-hours worked per day falls between 47.224 and 119.126.
D) We are 95% confident that the mean number of man-hours worked per day falls between 47.224 and 119.126 for all days in which 7,781 pieces of mail are processed and 644 checks are cashed.
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27
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):
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28
The confidence interval for the mean E(y) is narrower that the prediction interval for y.
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29
The table below shows data for n = 20 observations. The table below shows data for n = 20 observations.    The table below shows data for n = 20 observations.
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30
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):
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31
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary <strong>A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary   The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the tuition charged by the MBA program was $75,000 and the GMAT score was 675. The results are shown here: 95% confidence interval for E(Y): ($126,610, $136,640) 95% prediction interval for Y: ($90,113, $173,160) Which of the following interpretations is correct if you want to use the model to estimate Y for a single MBA program?</strong> A) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $126,610 and $136,640. B) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $90,113 and $173,16,30. C) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $126,610 and $136,640. D) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $90,113 and $173,16,30. The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the tuition charged by the MBA program was $75,000 and the GMAT score was 675. The results are shown here: 95% confidence interval for E(Y): ($126,610, $136,640) 95% prediction interval for Y: ($90,113, $173,160) Which of the following interpretations is correct if you want to use the model to estimate Y for a single MBA program?

A) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $126,610 and $136,640.
B) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $90,113 and $173,16,30.
C) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $126,610 and $136,640.
D) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $90,113 and
$173,16,30.
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32
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):
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33
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):
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34
In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x1) and the number of checks cashed per day (x2). Data collected for n = 20 working days were used to fit the model: In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x1) and the number of checks cashed per day (x2). Data collected for n = 20 working days were used to fit the model:
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35
Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive:
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36
In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x1) and the number of checks cashed per day (x2). Data collected for n = 20 working days were used to fit the model: In any production process in which one or more workers are engaged in a variety of tasks, the total time spent in production varies as a function of the size of the workpool and the level of output of the various activities. In a large metropolitan department store, it is believed that the number of man-hours worked (y) per day by the clerical staff depends on the number of pieces of mail processed per day (x1) and the number of checks cashed per day (x2). Data collected for n = 20 working days were used to fit the model:
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37
During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first three tests. To test this claim, multiple regression will be used to model Test 4 score (y), as a function of Test1 score (x1)\left( x _ { 1 } \right) , Test 2 score (x2)\left( x _ { 2 } \right) , and Test3 score (x3)\left( x _ { 3 } \right) . [Note: All test scores range from 200 to 800 , with higher scores indicative of a higher quality product.] Consider the model:
E(y)=β1+β1x1+β2x2+β3x3E ( y ) = \beta _ { 1 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 }
The global FF statistic is used to test the null hypothesis, H0:β1=β2=β3=0H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0 . Describe this hypothesis in words.

A) The model is not statistically useful for predicting Test4 score.
B) The model is statistically useful for predicting Test4 score.
C) The first three test scores are poor predictors of Test4 score.
D) The first three test scores are reliable predictors of Test4 score.
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38
During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first three tests. To test this claim, multiple regression will be used to model Test4 score (y), as a function of Test1 score (x1), Test 2 score (x2), and Test3 score (x3). [Note: All test scores range from 200 to 800, with higher scores indicative of a higher quality product.] Consider the model: E(y)=β1+β1x1+β2x2+β3x3E ( y ) = \beta _ { 1 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } The first-order model was fit to the data for each of 12 units sampled from the production line. A 95% prediction interval for Test4 score of a product with Test1 = 590, Test2 = 750, and Test3 = 710 is (583, 793). Interpret this result.

A) We are 95% confident that a product's Test4 score will fall between 583 and 793 points when the first three scores are 590, 750, and 710, respectively.
B) We are 95% confident that a product's Test4 score increases by an amount between 583 and 793 points for every 1 point increase in Test1 score, holding Test 2 and Test 3 score constant.
C) Since 0 is outside the interval, there is evidence of a linear relationship between Test4 score and any of the other test scores.
D) We are 95% confident that the mean Test4 score of all manufactured products falls between 583 and 793 points.
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39
As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):
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40
The rejection of the null hypothesis in a global F-test means that the model is the best model for providing reliable estimates and predictions.
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41
The complete second-order model with two quantitative independent variables does not allow for interaction between the two independent variables.
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42
A college admissions officer proposes to use regression to model a student's college GPA at graduation in terms of the following two variables: A college admissions officer proposes to use regression to model a student's college GPA at graduation in terms of the following two variables:   Explain how to determine if the relationship between college GPA and SAT score depends on the high school GPA. Explain how to determine if the relationship between college GPA and SAT score depends on the high school GPA.
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43
The concessions manager at a beachside park recorded the high temperature, the number of people at the park, and the number of bottles of water sold for each of 12 consecutive Saturdays. The data are shown below. The concessions manager at a beachside park recorded the high temperature, the number of people at the park, and the number of bottles of water sold for each of 12 consecutive Saturdays. The data are shown below.     12.5 Interaction Models 1 Write Interaction Model The concessions manager at a beachside park recorded the high temperature, the number of people at the park, and the number of bottles of water sold for each of 12 consecutive Saturdays. The data are shown below.     12.5 Interaction Models 1 Write Interaction Model 12.5 Interaction Models 1 Write Interaction Model
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44
In the quadratic model E(y)=β0+β1x+β2x2, a negative value of β1E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } , \text { a negative value of } \beta _ { 1 } indicates downward concavity.
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45
Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive: y=y = Retail PRICE (measured in dollars)
x1=x _ { 1 } = Microprocessor SPEED (measured in megahertz)
(Values in sample range from 10 to 40 )
x2=x _ { 2 } = CHIP size (measured in computer processing units)
(Values in sample range from 286 to 486 )
a first-order regression model was fit to the data. Part of the printout follows:
 Dep Var Predict Std Err Lower 95% Upper 95% OBS SPEED CHIP PRICE Value Predict Predict Predict Residual1332865099.04464.9260.7683942.74987.1634.1\begin{array}{lllllllll}\hline &&&\text { Dep Var }&\text {Predict }&\text {Std Err}&\text { Lower 95\%}&\text { Upper 95\% }\\ \text {OBS }&\text {SPEED }&\text {CHIP }&\text {PRICE}&\text { Value }&\text {Predict }&\text {Predict}&\text { Predict }&\text {Residual}\\1 & 33 & 286 & 5099.0 & 4464.9 & 260.768 & 3942.7 & 4987.1 & 634.1\\\hline \end{array}
Interpret the interval given in the printout.

A) We are 95% confident that the price of a single hard drive with 33 megahertz speed and 386 CPU falls between $3,943 and $4,987.
B) We are 95% confident that the price of a single hard drive falls between $3,943 and $4,987.
C) We are 95% confident that the average price of all hard drives falls between $3,943 and $4,987.
D) We are 95% confident that the average price of all hard drives with 33 megahertz speed and 386 CPU falls between $3,943 and $4,987.
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46
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary <strong>A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary   The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the tuition charged by the MBA program was $75,000 and the GMAT score was 675. The results are shown here: 95% confidence interval for E(Y): ($126,610, $136,640) 95% prediction interval for Y: ($90,113, $173,160) Which of the following interpretations is correct if you want to use the model to estimate E(Y) for all MBA programs?</strong> A) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $126,610 and $136,640. B) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $90,113 and $173,16,30. C) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $126,610 and $136,640. D) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $90,113 and $173,16,30. The model was then used to create 95% confidence and prediction intervals for y and for E(Y) when the tuition charged by the MBA program was $75,000 and the GMAT score was 675. The results are shown here: 95% confidence interval for E(Y): ($126,610, $136,640) 95% prediction interval for Y: ($90,113, $173,160) Which of the following interpretations is correct if you want to use the model to estimate E(Y) for all MBA programs?

A) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $126,610 and $136,640.
B) We are 95% confident that the average starting salary for graduates of a single MBA program that charges $75,000 in tuition and has an average GMAT score of 675 will fall between $90,113 and $173,16,30.
C) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $126,610 and $136,640.
D) We are 95% confident that the average of all starting salaries for graduates of all MBA programs that charge $75,000 in tuition and have an average GMAT score of 675 will fall between $90,113 and
$173,16,30.
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47
One of three surfaces is produced by a complete second-order model with two quantitative independent variables: a paraboloid that opens upward, a paraboloid that opens downward, or a saddle -shaped surface.
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48
Once interaction has been established between x1x _ { 1 } and x2x _ { 2 } , the first-order terms for x1x _ { 1 } and x2x _ { 2 } may be deleted from the regression model leaving the higher-order term containing the product of x1x _ { 1 } and x2x _ { 2 } .
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49
In an interaction model, the relationship between E(y)E ( y ) and x1x _ { 1 } is linear for each fixed value of x2x _ { 2 } but the slopes of the lines relating E(y)E ( y ) and x1x _ { 1 } may be different for two different fixed values of x2x _ { 2 } .
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50
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51
A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model
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52
A college admissions officer proposes to use regression to model a student's college GPA at graduation in terms of the following two variables: A college admissions officer proposes to use regression to model a student's college GPA at graduation in terms of the following two variables:   The admissions officer believes the relationship between college GPA and high school GPA is linear and the relationship between SAT score and college GPA is linear. She also believes that the relationship between college GPA and high school GPA depends on the student's SAT score. Write the regression model she should fit. 2 Test if Model is Useful for Predicting y The admissions officer believes the relationship between college GPA and high school GPA is linear and the relationship between SAT score and college GPA is linear. She also believes that the relationship between college GPA and high school GPA depends on the student's SAT score. Write the regression model she should fit. 2 Test if Model is Useful for Predicting y
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53
Which equation represents a complete second-order model for two quantitative independent variables? Which equation represents a complete second-order model for two quantitative independent variables?
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54
Consider the interaction model E(y)=7+3x14x2+5x1x2E ( y ) = 7 + 3 x _ { 1 } - 4 x _ { 2 } + 5 x _ { 1 } x _ { 2 } . Find the slope of the line relating E(y)E ( y ) and x1x _ { 1 } when x2=2x _ { 2 } = 2 when x2 = 2.

A) 13
B) 10
C) 1
D) 16
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55
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary
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56
Consider the partial printout below. Consider the partial printout below.   Is there evidence (at α = .05) that x1 and x2 interact? Explain. 12.6 Quadratic and Other Higher Order Models 1 Write and Interpret Second-Order Model Is there evidence (at α = .05) that x1 and x2 interact? Explain. 12.6 Quadratic and Other Higher Order Models 1 Write and Interpret Second-Order Model
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57
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary
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58
We decide to conduct a multiple regression analysis to predict the attendance at a major league baseball game. We use the size of the stadium as a quantitative independent variable and the type of game as a qualitative variable (with two levels - day game or night game). We hypothesize the following model: E(y)=β0+β1x1+β2x2+β3x3E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 }
Where x1=\mathrm { x } _ { 1 } = size of the stadium
x2=1\mathrm { x } _ { 2 } = 1 if a day game, 0 if a night game

A plot of the yx1y - x _ { 1 } relationship would show: :

A) Two parallel curves
B) Two non-parallel curves
C) Two non-parallel lines
D) Two parallel lines
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59
Consider the partial printout for an interaction regression analysis of the relationship between a dependent variable y and two independent variables x1 and x2. Consider the partial printout for an interaction regression analysis of the relationship between a dependent variable y and two independent variables x1 and x2.     3 Test for Interaction Between Two Variables Consider the partial printout for an interaction regression analysis of the relationship between a dependent variable y and two independent variables x1 and x2.     3 Test for Interaction Between Two Variables 3 Test for Interaction Between Two Variables
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60
 The independent variables x1 and x2 interact when the effect on E(y) of a change in x1 depends on x2\text { The independent variables } x _ { 1 } \text { and } x _ { 2 } \text { interact when the effect on } E ( y ) \text { of a change in } x _ { 1 } \text { depends on } x _ { 2 } \text {. }
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61
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model
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62
When testing the utility of the quadratic model E(y)=β0+β1x+β2x2E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } , the most important tests involve the null hypotheses H0:β0=0H _ { 0 } : \beta 0 = 0 and H0:β1=0H _ { 0 } : \beta _ { 1 } = 0 .
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63
A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model E(y)=β0+β1x+β2x2E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }
This model was fit to data collected for a sample of 32 clocks sold at auction; a portion of the printout follows:
 PARAMETER STANDARD  T FOR 0:  VARIABLES  ESTIMATE  ERROR  PARAMETER =0 PROB >T INTERCEPT 286.429.6629.64.0001X.31.065.14.0016XX.000067.00007.95.3600\begin{array}{lrrrr}\hline &\text { PARAMETER }& \text {STANDARD }& \text { T FOR 0: }\\\text { VARIABLES } & \text { ESTIMATE } & \text { ERROR } & \text { PARAMETER }=0 & \text { PROB }>|T|\\\text { INTERCEPT } & 286.42 & 9.66 & 29.64 & .0001 \\\mathrm{X} & -.31 & .06 & -5.14 & .0016 \\\mathrm{X} \cdot \mathrm{X} & .000067 & .00007 & .95 & .3600 \\\hline\end{array}

Give the pp -value for testing H0:β2=0H _ { 0 } : \beta _ { 2 } = 0 against Ha:β20H _ { a } : \beta 2 \neq 0 .

A) .36
B) .0016
C) .18
D) .05
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64
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model
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65
When using the model E(y) = β0 + β1x for one qualitative independent variable with a 0-1 coding convention, β1 represents the difference between the mean responses for the level assigned the value 1 and the base level.
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66
The complete second-order model The complete second-order model   data points. The printout is shown below.     3 Test if Model is Useful for Predicting y data points. The printout is shown below. The complete second-order model   data points. The printout is shown below.     3 Test if Model is Useful for Predicting y The complete second-order model   data points. The printout is shown below.     3 Test if Model is Useful for Predicting y 3 Test if Model is Useful for Predicting y
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67
A study of the top MBA programs attempted to predict y = the average starting salary (in $1000's) of graduates of the program based on x = the amount of tuition (in $1000's) charged by the program. After first considering a simple linear model, it was decided that a quadratic model should be proposed. Which of the following models proposes a 2nd-order quadratic relationship between x and y? A study of the top MBA programs attempted to predict y = the average starting salary (in $1000's) of graduates of the program based on x = the amount of tuition (in $1000's) charged by the program. After first considering a simple linear model, it was decided that a quadratic model should be proposed. Which of the following models proposes a 2nd-order quadratic relationship between x and y?
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68
What relationship between x and y is suggested by the scattergram? <strong>What relationship between x and y is suggested by the scattergram?  </strong> A) a quadratic relationship with downward concavity B) a quadratic relationship with upward concavity C) a linear relationship with positive slope D) a linear relationship with negative slope

A) a quadratic relationship with downward concavity
B) a quadratic relationship with upward concavity
C) a linear relationship with positive slope
D) a linear relationship with negative slope
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69
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary
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70
When modeling E(y) with a single qualitative independent variable, the number of 0-1 dummy variables in the model is equal to the number of levels of the qualitative variable.
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71
Consider the second-order model Consider the second-order model
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72
The table shows the profit y (in thousands of dollars) that a company made during a month when the price of its product was x dollars per unit. The table shows the profit y (in thousands of dollars) that a company made during a month when the price of its product was x dollars per unit.   4 Perform Quadratic Regression and Make Predictions 4 Perform Quadratic Regression and Make Predictions
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73
A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary A study of the top MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program and the average GMAT score of the program's students. The results of a regression analysis based on a sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary
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74
A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model E(y)=β0+β1x+β2x2E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }
This model was fit to data collected for a sample of 32 clocks sold at auction; a portion of the printout follows:
 PARAMETER STANDARD  T FOR 0:  VARIABLES  ESTIMATE  ERROR  PARAMETER =0 PROB >T INTERCEPT 286.429.6629.64.0001X.31.065.14.0016XX.000067.00007.95.3600\begin{array}{lrrrr}\hline &\text { PARAMETER }& \text {STANDARD }& \text { T FOR 0: }\\\text { VARIABLES } & \text { ESTIMATE } & \text { ERROR } & \text { PARAMETER }=0 & \text { PROB }>|T|\\\text { INTERCEPT } & 286.42 & 9.66 & 29.64 & .0001 \\\mathrm{X} & -.31 & .06 & -5.14 & .0016 \\\mathrm{X} \cdot \mathrm{X} & .000067 & .00007 & .95 & .3600 \\\hline\end{array}

Find the pp -value for testing H0:β2=0H _ { 0 } : \beta _ { 2 } = 0 against Ha:β2>0H _ { \mathbf { a } } : \beta _ { 2 } > 0 .

A) .18
B) .36
C) .0016
D) .05
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75
A graphing calculator was used to fit the model E(y) = ?0 + ?1x + ?2x2 to a set of data. The resulting screen is shown below.  <strong>A graphing calculator was used to fit the model E(y) = ?0 + ?1x + ?2x2 to a set of data. The resulting screen is shown below.   Which number on the screen represents the estimator of  \beta _ { 2 }  ?</strong> A) .9286 B) 5.5 C) 11 D) .9405  Which number on the screen represents the estimator of β2\beta _ { 2 } ?

A) .9286
B) 5.5
C) 11
D) .9405
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76
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model
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77
Consider the data given in the table below. Consider the data given in the table below.   a. Plot the data on a scattergram. Does a quadratic model seem to be a good fit for the data? Explain. b. Use the method of least squares to find a quadratic prediction equation. c. Graph the prediction equation on your scattergram. 12.7 Qualitative (Dummy) Variable Models 1 Write and Interpret Model with Qualitative Variables a. Plot the data on a scattergram. Does a quadratic model seem to be a good fit for the data? Explain. b. Use the method of least squares to find a quadratic prediction equation. c. Graph the prediction equation on your scattergram. 12.7 Qualitative (Dummy) Variable Models 1 Write and Interpret Model with Qualitative Variables
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78
Consider the data given in the table below. Consider the data given in the table below.   Plot the data on a scattergram. Does a second-order model seem to be a good fit for the data? Explain. Plot the data on a scattergram. Does a second-order model seem to be a good fit for the data? Explain.
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79
A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant) rate. Thus, the model proposed to best explain auction price (y, in dollars) by number of bidders (x) is the quadratic model
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80
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status the owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model
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